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Mathematics
Problem
Let
A
=
[
0
1
0
1
0
0
0
0
1
]
A = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix}
A
=
0
1
0
1
0
0
0
0
1
. Then the number of
3
×
3
3 \times 3
3
×
3
matrices
B
B
B
with entries from the set
{
1
,
2
,
3
,
4
,
5
}
\{1, 2, 3, 4, 5\}
{
1
,
2
,
3
,
4
,
5
}
and satisfying
A
B
=
B
A
AB = BA
A
B
=
B
A
is ________. [NA, July 22, 2021 (II)]
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